Education Technology

Complex Spirals

Updated on 05/03/2021

Activity Overview

In this short focused investigation students explore what happens when a complex number is repeatedly raised to a power. Students then move onto Partial Sums and some of the geometry involved. 


Students relate the magnitude of the complex number to the spiral, spiral in or spiral out. Students also explore the angle between successive terms and triangles formed; leading to an understanding of complex numbers in polar form.


  • Magnitude
  • Real component
  • Imaginary component
  • Spiral in or out

About the Lesson

Watch Activity Tutorial

Students start by plotting simple complex numbers raised to a power. Successive powers create a pattern (spiral) under certain conditions. Students explore the spiral, conditions and then partial sums and their spirals.